Contraction Analysis of Power System Dynamics Using Time-Varying OMIB Equivalents

Abstract

The paper presents a non-traditional approach to assessment of global dynamics in power systems. The method is based on nonlinear contraction analysis of a generalized time-varying, one-machine infinite bus (OMIB) equivalent of the system, and can be applied to establish global contraction for the nonlinear system response following perturbations. It has a potential to complement traditional stability studies as it does not depend on the precise knowledge of the (post-fault) system equilibrium. In our procedure, a time-varying OMIB model of the system is constructed first. Based upon this model, nonlinear contraction theory is used next to investigate the onset of the divergence of system trajectories. In particular, an OMIB-based metric is suggested that accounts for nonlinear and time-varying behavior and allows contraction analysis of system dynamics and the study of robustness properties. The developed procedures are tested on a large-scale power system model that exhibits complex inter-area oscillations following major contingencies. Results from both contraction and conventional analyses are presented.